QCD threshold corrections for gluino pair production at hadron colliders

TL;DR

This work delivers threshold-enhanced QCD predictions for gluino pair production at hadron colliders at $NNLO$ accuracy in the threshold limit, achieved by computing one-loop hard matching coefficients to obtain $NNLL$ resummed cross sections. The approach combines Mellin-space threshold resummation with explicit near-threshold matching, yielding approximate $NNLO$ hadronic cross sections for gluino pairs with reduced scale uncertainties. The phenomenology at the LHC shows a $~15$–$20 ext{\%}$ increase over NLO and a remaining PDF-driven uncertainty that can be sizable depending on the PDF set used. These results align gluino production with the precision level attained for squark-antisquark production and have meaningful implications for SUSY searches and exclusion limits given current and future LHC data.

Abstract

We present the complete threshold enhanced predictions in QCD for the total cross section of gluino pair production at hadron colliders at next-to-next-to-leading order. Thanks to the computation of the required one-loop hard matching coefficients our results are accurate to the next-to-next-to-leading logarithm. In a brief phenomenological study we provide predictions for the total hadronic cross sections at the LHC and we discuss the uncertainties arising from scale variations and the parton distribution functions.

Figures (7)

• Figure 1: Feynman diagrams for the production of a gluino pair $\widetilde{g}\,\widetilde{g}$ via $q \bar{q}$ annihilation (diagrams (a) - (c)) and $gg$ annihilation (diagrams (d) - (f)) at LO.
• Figure 2: The scaling functions $f^{(ij)}_{gg}$ and $f^{(ij)}_{q \bar{q}}$ with $i = 0,1,2$ and $j\le i$ in the $\overline{\rm MS}$-scheme. The masses are $m_{\widetilde{g}} = 750\,\,\mathrm{GeV}$ and $m_{\widetilde{q}} = 600\,\,\mathrm{GeV}$.
• Figure 3: Scaling function $f^{(10)}_{gg,B}$ (threshold approximation with exact Born function) for $0.3<r<2$.
• Figure 4: Total hadronic cross section and its theoretical uncertainty at the LHC for three different center of mass energies (7$\,\mathrm{TeV}$ (upper figure), 8 $\,\mathrm{TeV}$ (central figure), and 14$\,\mathrm{TeV}$ (lower figure)) at LO (blue bands), NLO (green bands), and NNLO$_{\text{approx}}$ (purple lines) as a function of the gluino mass. The masses of the squarks and the stop are set to $m_{\widetilde{q}} = 4/5m_{\widetilde{g}}$. At NNLO$_{\text{approx}}$, the theoretical uncertainty has shrunk to a small band.
• Figure 5: Scale dependence of the total hadronic cross section at the LHC with $14\,\mathrm{TeV}$ for $m_{\widetilde{g}} = 750\,\,\mathrm{GeV}$ and $m_{\widetilde{q}} = 600\,\,\mathrm{GeV}$. The vertical bars indicate the total scale variation in the range $[m_{\widetilde{g}}/2,2\*m_{\widetilde{g}}]$, the vertical dashed gray line in the middle of the figure indicates the cross section at the nominal scale $\mu = m_{\widetilde{g}}$.